My facebook push notification doesn't work since I got my Galaxy S and recently I found a solution to it. Those with the push notification problem can try it out.

Steps:

1) Go to Settings->Manage Applications->Facebook
2) Clear data and Clear cache
3) login to www.facebook.com via PC
4) Go to Accounts->Accounts Settings
5) Click "Deactivate" Yes, DEACTIVATE, don't worry, you won't lose anything.
6) Wait for email confirmation that you've deactivated your facebook.
7) Re-login back facebook via PC.
8) Re-login back facebook via Facebook App.


With these steps, my push notification is working.

I don't guarantee it work for you, but it works for me. I hold no responsibilities if anything went wrong with your phone.